Improvement of infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem

Abstract

This paper presents some improved infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem, which comprises the Navier--Stokes equations for the flow in a two-dimensional flat torus under a special driving force. These estimations and the basic idea behind them play important roles in accurate enclosing of solutions for such type of nonlinear differential equations. Several comparisons of concrete values confirm the effectiveness of the presented approach.